i think you did a great job and it is full of good suggestions.
By invading one in the diplomatic missions for the other, you can quickly advance to ally status with the faction you are trying to win - a more proactive approach that allows you to reach ally status in less time. I did not go to war with another faction, but I do not want to wait for building a relationship by defending the marina etc. I think that to win the war we do not need support of 3 factions, it is enough to support 1 or 2
I think you did well with this guide